Note on E representations in
C6 character table



4 irreducible representations of point group C6 have complex values. 2 two-dimensional real-valued representations E can be constructed as direct sum of the 2 pairs complex plus conjugate complex irreducible representation.

E1 = E1a ⊕ E1b
E2 = E2a ⊕ E2b


ε=exp(2πi/6)
C6 E C6 C3 C2 (C3)2 (C6)5
A 1 1 1 1 1 1
B 1 -1 1 -1 1 -1
E1 E1a
E1b
1
1
ε*
ε*
*
*
-1
-1
*
*
ε*
ε*
E2 E2a
E2b
1
1
*
*
*
*
1
1
*
*
*
*


Obviously the E representations are reducible. Nevertheless the E representations are treated often as irreducible representations and are called real-valued or pseudo irreducible representations. One should keep in mind that general statements for character tables fail for real-valued representations. For example:



Last update August, 12th 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement